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寻找匹配的夫妻以最大限度地提高全球幸福感

[英]Find matching couples to maximize global happiness

原文 2018-02-15 21:18:01 7 1 python/ algorithm/ numpy/ matching

A belated Valentines day question for you all:一个迟来的情人节问题给大家：

Suppose we have M men an W women, and they are all heterosexual.假设我们有 M 个男人和 W 个女人，他们都是异性恋。 We have a (MxW) matrix A where A[m, w] quantifies how happy the couple (m, w) would be if married.我们有一个 (MxW) 矩阵 A，其中A[m, w]量化了这对夫妇(m, w)结婚后的幸福程度。

How can we pair the couples so that the global maximum happiness is achieved?我们如何配对夫妻才能实现全球最大的幸福？ (ie I'm looking to produce a length min(M, W) array of 2-tuples identifying who should be paired up, such that sum(A[m, w] for m, w in couples) is maximized, and each m and each w is only used once. （即，我希望生成一个长度为min(M, W)的 2 元组数组，以确定谁应该配对，这样sum(A[m, w] for m, w in couples)被最大化，并且每个m并且每个w只使用一次。

Note 1: Ideally I'm looking for a fast numpy implementation, but that's kind of secondary to finding the right algorithm.注 1：理想情况下，我正在寻找一种快速的 numpy 实现，但这对于找到正确的算法来说是次要的。
Note 2: This is similar, but not the same as the Stable Marriage Problem , where you specify each person's ranked preferences instead of a happiness value.注 2：这与稳定婚姻问题类似，但不同的是，您指定每个人的排名偏好而不是幸福值。

1 个解决方案

Well, thanks to the commenters for pointing out that this is the Assignment Problem , and is usually described in terms of workers and jobs.好吧，感谢评论者指出这是分配问题，通常以工人和工作的形式描述。

Scipy has a function that solves it using the Hungarian Algorithm. Scipy 有一个使用匈牙利算法解决它的函数。